Risk Of Ruin: How Much Bankroll Is Enough

The Formula

The Standard Approximation Says Risk Of Ruin Equals E Raised To The Power Of Minus Two Times Your Win Rate Times Your Bankroll, Divided By The Variance Of Your Results. Win Rate, Standard Deviation And Bankroll All Have To Be Measured In The Same Unit, Big Blinds Here, And Win Rate And Standard Deviation Over The Same Number Of Hands.

The Figures Below Assume A Win Rate Of 5 Big Blinds Per 100 Hands, A Standard Deviation Of 100 Big Blinds Per 100 Hands, And Buy Ins Of 100 Big Blinds. They Are Illustrative Assumptions Chosen For The Example, Not Typical Or Measured Values. Doubling The Bankroll Squares The Risk Of Ruin, Which Is Why The Numbers Shrink So Quickly.

Smarter.Poker Itself Is Free To Play With Play Credit Only And No Real Money Gambling, So Nothing Here Is About Money On This Platform. These Are The Rules Players Use For Poker Bankrolls Elsewhere. The Bankroll Manager Here Is A Record Of The Sessions You Enter Yourself, Wherever You Played Them, So You Can Practise The Record Keeping These Rules Depend On; It Handles No Money.

What The Formula Assumes

The Formula Treats Your Results As A Smooth Random Walk With A Win Rate That Is Known Exactly And Never Changes. Neither Is True. Your Real Win Rate Is An Estimate With A Wide Margin Of Error Unless You Have Played A Very Large Number Of Hands, And It Changes As You Improve, As Games Change And As You Tilt.

Because A Real Win Rate Is Uncertain, The Honest Use Of The Formula Is To Try Several Win Rates, Including A Much Lower One Than You Hope For, And To Keep A Bankroll That Is Safe Against The Pessimistic Case. A Player Whose True Win Rate Is Zero Or Negative Has A Risk Of Ruin Of 100% No Matter How Large The Bankroll Is.

Using It Well

Pick The Risk You Can Accept First, Then Work Out The Bankroll. Many Players Are Comfortable With A Risk Of A Few Percent, Others Want Less Than One Percent. The Formula Turns That Choice Into A Number Of Buy Ins For Your Own Win Rate And Variance.

Recalculate As Your Data Grows. After A Few Hundred Thousand Hands Your Estimates Will Be Much Tighter, And The Right Bankroll May Move Up Or Down. And Remember That A Bankroll Can Be Replenished Only If You Have Money Outside Poker To Do It With; If You Do Not, Be More Conservative.

Practise It On Smarter.Poker

The Answer Above Is Complete. When You Want To Drill It, These Are The Matching Training Tools.

• Play Variance Zen The Training Game For This Lesson.
• Open The Bankroll Manager
• Open Jarvis Training Insights Jarvis Explains Your Training Decisions In Words.